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Homoclinic bifurcation analysis of a class of conveyor belt systems with dry friction and impact

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  • Peng, Ruyue
  • Li, Qunhong
  • Zhang, Wei

Abstract

The non-smooth systems that have been found to exhibit homoclinic bifurcation and subharmonic bifurcation so far are mainly impact vibration systems and dry friction systems. However, for friction impact systems concerned by many scholars, to the best of our knowledge, there is no literature that considers the effects of impact and friction on homoclinic bifurcation and subharmonic bifurcation simultaneously. For friction impact systems, the complexity of homoclinic and subharmonic bifurcations is higher due to the influence of two non-smooth factors: impact and friction. This paper utilizes a combination of analytical and numerical methods to study the chaotic motion and subharmonic bifurcation in a conveyor belt system with bilateral rigid constraints connected by oblique springs and dampers. By applying the Melnikov method to the non-smooth conveyor belt system with friction and impact, the piecewise Melnikov function of homoclinic orbits, which depends on the conveyor belt speed, is analytically obtained. The threshold conditions for chaos and subharmonic bifurcation in the system are derived. Additionally, critical regions are plotted in multiple parameter spaces based on these threshold conditions to differentiate between chaotic and non-chaotic regions. The critical parameter region for the occurrence of subharmonic bifurcation in the friction impact system is determined using the Melnikov method, and the relationship between subharmonic bifurcation and chaos is discussed. The effects of parameters such as the damping coefficient, excitation frequency, excitation amplitude, impact coefficient of restitution, dry friction, and belt speed on chaotic motion and subharmonic bifurcation are studied based on the derived threshold conditions. The validity of the theoretical results is further verified through numerical simulations.

Suggested Citation

  • Peng, Ruyue & Li, Qunhong & Zhang, Wei, 2024. "Homoclinic bifurcation analysis of a class of conveyor belt systems with dry friction and impact," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924000201
    DOI: 10.1016/j.chaos.2024.114469
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    References listed on IDEAS

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    1. Zheng, Yanxiao & Li, Qunhong & Zhang, Wei & Lei, Jinfeng, 2023. "Three-dimensional mapping analysis of a capsule system with bilateral elastic constraints," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Guo, Xiuying & Tian, Ruilan & Xue, Qiang & Zhang, Xiaolong, 2022. "Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
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    5. Zhang, Yifeng & Xu, Huidong & Zhang, Jianwen, 2023. "Global dynamics for impacting cantilever beam supported by oblique springs," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    6. Peng, Yuanyuan & Fan, Jinjun & Gao, Min & Li, Jianping, 2021. "Discontinuous dynamics of an asymmetric 2-DOF friction oscillator with elastic and rigid impacts," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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